##### This material has been published in
Experiment. Math. **12** (2003),
441-456,
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## Gert Almkvist, Christian Krattenthaler and Joakim Petersson

# Some new formulas for pi

### (28 pages)

**Abstract.**
We show how to find arbitrarily fast convergent
series expansions for *\pi* of the
form
*\pi=\sum_{n=0}^\infty {S(n)}\big/{\binom{mn}{pn}a^n}*, where
*S*(*n*) is some polynomial in *n* (depending on
*m*,*p*,*a*).
We prove that there exist such
expansions for *m*=8*k*, *p*=4*k*,
*a*=(-4)^{k}, for any *k*, and give
explicit examples for such expansions for small values of *m*,
*p* and *a*.

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